| Contents |
| The Flaschka transformation has been introduced historically by Flaschka and Manakov in
the early 70s in order to provide a Lax pair for the Toda lattice integrable system. It turns out
that this is just an instance of a map that provides a symplectomorphism between certain coadjoint orbits and magnetic cotangent bundles. If the structure of the coadjoint orbit is simple enough, then this method provides global canonical coordinates; this is the case for the finite
Toda systems associated to an arbitrary Dynkin diagram. We shall discuss the general geometric setup leading to this map, connect it to a momentum map and to Pukanszky's conditions. The example of the Toda lattice will be presented as well as other ones that,
classically, do not fall in the same category of orbits. |
|